As far as I can determine, lactose, and the monosaccharide galactose have few biological uses outside of mammalian lactation. It not only required enzymes for its production, but enzymes in offspring for its digestion, suggesting that it serves some specific purpose. Yet intuitively, it seems like it would have been significantly easier to just concentrate glucose from the blood or generate a disaccharide readily found in the diet like sucrose, for which digestive enzymes already existed.

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As it happens someone has just published a theory about this. To save you following the link, I reproduce the abstract below.

I must admit that I had never realised that lactose is synthesised within the organelles of the secretory pathway (β4-galactosyltransferase is a Golgi enzyme and α-lactalbumin is, of course, a whey protein, so is in transit through the pathway). This may go part of the way to answering your question: by having a disaccharide that is made within the Golgi, the cells of the mammary gland will effectively partition their glucose metabolism between the cytoplasm and that destined for secretion as lactose (transported into the Golgi lumen).

Mammalian milk or colostrum contains up to 10% of carbohydrate, of which free lactose usually constitutes more than 80%. Lactose is synthesized within lactating mammary glands from uridine diphosphate galactose (UDP-Gal) and glucose by a transgalactosylation catalysed by a complex of β4-galactosyltransferase and α-lactalbumin (α-LA). α-LA is believed to have evolved from C-type lysozyme. Mammalian milk or colostrum usually contains a variety of oligosaccharides in addition to free lactose. Each oligosaccharide has a lactose unit at its reducing end; this unit acts as a precursor that is essential for its biosynthesis. It is generally believed that milk oligosaccharides act as prebiotics and also as receptor analogues that act as anti-infection factors. We propose the following hypothesis. The proto-lacteal secretions of the primitive mammary glands of the common ancestor of mammals contained fat and protein including lysozyme, but no lactose or oligosaccharides because of the absence of α-LA. When α-LA first appeared as a result of its evolution from lysozyme, its content within the lactating mammary glands was low and lactose was therefore synthesized at a slow rate. Because of the presence of glycosyltransferases, almost all of the nascent lactose was utilized for the biosynthesis of oligosaccharides. The predominant saccharides in the proto-lacteal secretions or primitive milk produced by this common ancestor were therefore oligosaccharides rather than free lactose. Subsequent to this initial period, the oligosaccharides began to serve as anti-infection factors. They were then recruited as a significant energy source for the neonate, which was achieved by an increase in the synthesis of α-LA. This produced a concomitant increase in the concentration of lactose in the milk, and lactose therefore became an important energy source for most eutherians, whereas oligosaccharides continued to serve mainly as anti-microbial agents. Lactose, in addition, began to act as an osmoregulatory molecule, controlling the milk volume. Studies on the chemical structures of the milk oligosaccharides of a variety of mammalian species suggest that human milk or colostrum is unique in that oligosaccharides containing lacto-N-biose I (LNB) (Gal(β1 → 3)GlcNAc, type I) predominate over those containing N-acetyllactosamine (Gal(β1 → 4)GlcNAc, type II), whereas in other species only type II oligosaccharides are found or else they predominate over type I oligosaccharides. It can be hypothesized that this feature may have a selective advantage in that it may promote the growth of beneficial colonic bacteria, Bifidobacteria, in the human infant colon.